1. Field of the Invention
The present invention is directed to a method for generating a displayable image from data obtained by irradiation of an examination subject in a computed tomography apparatus, and in particular to a method for image reconstruction suitable for use in such a computed tomography apparatus.
2. Description of the Prior Art
In computed tomography, CT images can be reconstructed by the linogram method. The linogram method was introduced by P. Edholm in 1987, see P. R. Edholm, G. T. Herman, "Linograms in Image Reconstruction from Projections,"IEEE Trans. on Med. Imag., vol. MI-6, No. 4, 1987, pp. 301-307. It is a special Fourier reconstruction method that functions entirely without interpolation in the frequency space. A disadvantage of the usual Fourier reconstruction method is that after the one-dimensional fast Fourier transformation of the measured projections f.sub.lk, discrete spectrum values are defined on a polar grid. The transition to the Cartesian grid in the frequency space takes place by means of a two-dimensional interpolation, which leads to flawed images if insufficient care is taken. The essential idea of the linogram method is to organize discrete spectrum values on a "quasi-Cartesian" grid from the outset through suitable measures, so that interpolation in the frequency space is no longer necessary.
In the known linogram method, a spectrum is always generated that corresponds to the image in the overall measurement field with the diameter D.sub.M. As in the direct Fourier transformation methods, this results in that a very large number of points must be reckoned with in the frequency space with matrices. In the original linogram method, spectral values with a fixed grid ##EQU1## result in the .rho..sub.x direction in the angle region [-45.degree., 45.degree.] in the frequency space, while spectral values with a fixed grid ##EQU2## result in the .rho..sub.y direction in the angle region [45.degree., 135.degree.] (.rho..sub.x and .rho..sub.y are the Cartesian frequency variables). If there are N.sub.p =2048 projections in the angle region [-45.degree., 135.degree.] with N=1024 measurement values per projection in the sampling grid ##EQU3## this means that the two sub-matrices for [-45.degree., 45.degree.] or [45.degree., 135.degree.] in the frequency space each have ##EQU4##
If the method is to be of practical importance, it must be possible to reconstruct arbitrary eccentric image segments. For this purpose, in the known linogram method chirp-z transformations are undertaken on the desired image segment D.sub.B .multidot.D.sub.B with N.sub.Pix .multidot.N.sub.pix image elements in the grid ##EQU5## on the basis of the two sub-matrices, in both the .rho..sub.x and the .rho..sub.y directions. This step is so expensive in terms of processing outlay that it far outweighs the advantage of the lack of interpolation in the frequency space.